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Associative Errors Associative Errors
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Abstract
Pre-adolescents often come to analogy solution via free association instead
of logical reasoning, and this tendency has been related to non-adaptive
learning strategies and slower intellectual growth. The purpose of this
study was to investigate the cognitive processes underlying the associative
response strategy in analogy solution. 112 fifth graders were administered
a battery of tests designed to assess different components of analogical
reasoning. The Children's Associative Responding Test (CART), a verbal
analogies test which yields associative and non-associative error scores,
was also administered. Factor analysis of this battery resulted in four
primary factors: vocabulary, encoding and retrieval processes, discovery
of semantic relations and semantic flexibility, and response evaluation.
A higher order general factor was also found. Further regression analyses
showed that only the mapping relations component did not significantly
predict the two CART scores. Despite considerable criterion overlap,
vocabulary and discovery of semantic relations were more highly related to
non-associative errors, and working memory and semantic flexibility were
more highly related to associative errors.
Associative Errors in Children's Analogical Reasoning:
A Cognitive Process Analysis
A very common error in children's attempts to solve verbal analogies
is to respond with a word strongly associated with the third term in the
analogy. For instance, in "dog is to puppy as cow is to ----," many
children will respond with "milk," a strong associate of "cow" but an
incorrect answer. This has come to be known as the associative response
phenomenon. While some researchers have argued that association is the
primary component of analogy solution for all age groups (e.g., Gentile,
Tedesco-Stratton, Davis, Lund, & Agunanne, 1977; Willner, 1964), the
empirical evidence supports a developmental shift in strategy. For
instance, Achenbach (1971) found that associative errors of this type
decreased as adolescence progressed. Similarly, Sternberg and Nigro (1980)
found that third and sixth grade students relied heavily upon association
to solve analogies whereas ninth grade and college students relied instead
upon inference.
The associative response phenomenon appears to have significance
within developmental level as well. Evidence has accrued suggesting that
students who make more associative errors than non-associative errors
achieve less well in school as measured by grade point average (Achenbach,
1969), with this achievement gap increasing with time, as longitudinal
studies have shown (Achenbach, 1971, 1975). Moreover, there is indication
that level of associative responding moderates the school achievement-
intelligence relationship (Achenbach, 1970a, 1970b, 1971; Tirre, Note 1).
From the Tirre (Note 1) analyses it was found that associative responders
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were predicted to achieve less than non-associative responders of equal
intelligence in reading, language arts, and mathematics. These findings
corroborate earlier studies by Achenbach (1970a, 1970b, 1971).
A study by Kerner and Achenbach (1971) suggests that associative
responders employ processes different from those of non-associative
students when attempting to learn in school. They found that the best
predictors of grades for associative responders were two rote-associative
tasks: recall of categorizable items and recall of non-categorizable
items. Two tasks involving reasoning, i.e., concept formation and
paragraph comprehension, were not predictive at all. Precisely the
opposite results were found for the non-associative students.
Interestingly, the recall tasks were substantially correlated for the
associative students and uncorrelated for the non-associative students,
though the difference between these correlations was not quite significant.
This latter finding suggests that associative students could have
approached the two lists in like manners, perhaps not taking advantage of
the structure in the categorizable lists. Taken together, these results
imply that students who employ the associative strategy in verbal analogy
problems may also fail to employ conceptual processes in other appropriate
learning situations. If more were known about the cognitive nature of the
associative strategy we would be in a better position to explain existing
data and to make more informed hypotheses about the learning processes of
associative students.
The purpose of this study was to compare and contrast the cognitive
components of associative and non-associative errors on analogies as
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measured by the Children's Associative Responding Test (CART) (Achenbach,
1970a). The CART consists of 68 verbal analogies, half of which include an
associative foil, i.e., a distractor highly associated with the third term
of the analogy. The other half of the items do not have strong associates
as distractors so that association should not facilitate or impede
solution. The two item types induce the student to attempt solution in
different ways, i.e., in an associative manner by the associative foil
items, or in a more logic-based manner by the items in which associations
are less available. By examining the differences between these scores,
much can be learned of the unique nature of associative responding.
The Sternberg (1977) componential framework was adopted in this study.
Previous studies employing this framework but different methodologies have
demonstrated its usefulness (Whitely & Barnes, 1979). In this application,
the following were considered as components of analogical reasoning:
semantic knowledge, working memory, encoding and retrieval, semantic
flexibility, inference, mapping relations, and the response evaluation part
of the application component. Each of these components could be
hypothesized to be the locus of processing failure leading to the
associative response. Within some of these components there could be
several mechanisms or subcomponents responsible for processing failure.
Semantic Knowledge Hypothesis
First of all, it could be hypothesized that the associative response
is due to a failure to understand the analogy terms. Inadequate semantic
knowledge precludes meaningful comparison of analogy term attributes in
inferring and mapping relations as well as response evaluation. In an
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experimental study vocabulary difficulty should be controlled; in a
correlational study, it must be partialed out as an initial step.
Encoding Hypotheses
Three hypotheses concerning the role of encoding in the associative
response can be entertained. The first of these is that despite adequate
semantic knowledge, semantic encoding of analogy terms is too "shallow" and
this leads to associative errors (Craik & Lockhart, 1971). All subsequent
component operations would be adversely affected by inadequate encoding.
If encoding is too "shallow," i.e., the semantic attributes of the analogy
terms are not properly accessed and attended to, then we should expect
subsequent operations, which are carried out upon the products of encoding,
to suffer as well.
A related hypothesis is that associative responding results when the
student is inflexible in thinking about the meanings of words. The primary
meaning of a word might be accessed and then be too difficult to discard
when it is the secondary meaning of a word that is really needed.
Yet another encoding-related hypothesis is that limited working memory
adversely affects the encoding process. Smaller capacity would make the
encoding process more difficult, and make attribute comparison processes in
inferring and mapping relations more difficult as well. Encoding of
analogy terms may have occurred without mishap. However, if the student
cannot keep these attributes in consciousness, then inference and other
processes will be adversely affected.
Inference Hypotheses
The fifth hypothesis is that a faltering of processing during the
inference stage leads to the associative response. Consider the typical
analogy form A is to B as C is to D. If a student has only a vague notion
of how A and B are related in the domain (A is to B) then she/he will have
a lower criterion of acceptability for a relationship between C and D in
the range.
There are at least three ways in which the inference process could
lead to the associative error. First of all, students may have a
"conceptual style" that predisposes them to look for a particular kind of
relationship at the expense of other types of relationships (Sigel, 1967).
Sigel describes three different styles. The "relational-contextual" style
would appear to be most at odds with analogy solution. In this case, the
child groups objects together because they are functionally or thematically
interdependent, e.g., horse and coach go together because the horse pulls
the coach. Contrast this with the "inferential-categorical" style in which
sortings are made on the basis of some inferred, shared feature. In a
pilot study with 29 sixth-grade students, the Sigel (1967) Conceptual Style
test was administered along with the CART. No significant correlations
were found between the tests, ruling out any role of conceptual style in
associative responding.
However, we may still hypothesize that faulty inferences are made when
the child has inadequate knowledge of the types of semantic relations
typically found in analogies. Whitely (1977) identified seven types of
semantic relationships in analogies using latent partition analysis.
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Instruction on these relationships can improve analogy performance (Whitely
& Dawis, 1974) suggesting that the relational education or inference
process is guided in some manner by knowledge of what kinds of relations
are likely to be found. An obvious example of this is the problem in which
a relation between "pot" and "top" is to be discovered and then applied to
"ton" to complete the analogy. Knowledge that word pattern analogies are
legitimate types would direct the person away from semantic comparison of
attributes and towards orthographic comparison leading to the answer "not."
The third way the inference process could go awry and affect later
processing is through a failure to compare and contrast semantic
attributes, given that the student is aware that this is the appropriate
strategy. In Sternberg's theory, inference is a matter of comparing the
attribute lists of the A and B terms. For instance, "wolf" and "dog" share
a number of attributes subsumed under the concept "canine." Let us suppose
that on only one dimension "tameness" do they really differ. List
comparison allows the inference "a wolf is like a wild dog." The
hypothesis then, is that skill at such semantic processing should be highly
negatively correlated with associative errors.
Mapping Hypothesis
We may also hypothesize that associative responding is the natural
consequence of treating the analogy range as an isolated word pair, i.e.,
the relation found in the domain is never mapped onto the range. Gallagher
and Wright (Note 2, 1979) argue that analogy errors result from an
inadequate understanding of higher order relationships, i.e., relations
between relations. They noted that symmetric explanations of analogies,
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i.e., explanations which demonstrate the symmetry or balance between domain
and range, are correlated highly with correct solution and increase in
frequency and in sophistication as the child leaves childhood and
progresses through adolescence (see also Levinson & Carpenter, 1974). As
examples of symmetric explanations consider the following seventh-grade
responses to Engine is to Car as Man is to Bicycle:
"Because man is a bicycle's engine."
"The first word provides power to the second."
Contrast these rule-specifications to the following fourth-grade responses
which focus on the analogy range:
"A man makes a bike go."
"A man rides a bike."
In the present study, the Gallagher and Wright Written Analogical Reasoning
Test (WART) was employed to determine the relation between the
understanding of symmetric relations and associative responding.
Impulsiveness Hypothesis
Lastly, it was hypothesized that carelessness in evaluating
alternative solutions to the analogy results in associative errors. Such
carelessness could be another manifestation of an impulsive cognitive style
(Kagan, Rossman, Day, Albert, & Phillips, 1964). To test this hypothesis,
scores on the Matching Familiar Figures test were correlated with the CART
criteria. Impulsiveness is indicated by fast, inaccurate selection of
figures and reflectiveness is indicated by slow, accurate selection. A
significant interaction between speed and accuracy should be noted if
impulsiveness plays a role in associative responding.
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Each of the six components of analogical reasoning was measured by a
paper-and-pencil test. Two questions were asked of the data. The first
was whether the tasks representing the components did indeed cluster in the
hypothesized manner. This was determined with factor analysis. The second
question concerned how the CART associative and non-associative scores are
distinguished in terms of contributions by each of the components.
Regression models were employed to answer this question.
Method
Subjects
The sample consisted of 127 fifth-grade students. Fifty-five children
were tested in a parochial school in suburban Chicago and seventy-two
children in a public school in suburban St. Louis. Nearly all the children
in the Chicago area school were White, whereas about 50% of the children in
the St. Louis school were Black. Deleting cases with incomplete data left
112 cases.
Procedure
Nine tests were administered to the children in their regular
classrooms. From these nine tests were derived two measures of vocabulary
knowledge, three measures of verbal inductive reasoning, a measure of the
mapping component, and latency and error scores on the Matching Familiar
Figures Test assessing impulsiveness-reflectiveness. Scores on two tests
of vocabulary were obtained from school files. Two measures of different
aspects of analogical reasoning were obtained from the CART: associative
and non-associative errors. Testing was carried out in two one-hour
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sessions, one in the morning and one in the afternoon. With the exception
of the Matching Familiar Figures test, all tests were group-administered.
For all tests instructions were written to explain the task to the
student, giving several examples which could be worked on individually and
then together as a group. Time limits were announced for the tests.
Experimental Tasks
Measures of semantic knowledge. The Vocabulary test was designed to
assess two aspects of semantic knowledge. The first aspect measured is the
ability to select the meaning of a word from among several close
alternatives (VOCABR). The second aspect measured is semantic flexibility
(SEMFLEX), or the ability to find a second meaning of a word which is less
common and which is embedded in a context more consistent with the primary
meaning of the word. A sample item will make this clearer:
Fire: flames smoke water hydrant shoot.
"Flames" is closest to the primary meaning of fire. It is embedded among
other words consistent with the context of flames, e.g., smoke, water,
hydrant. The secondary meaning of fire is "shoot," as in to shoot or fire
a gun. Instructions were to circle the first meaning found one time, and
the second meaning, if found, two times. This test was inspired by a test
devised by MacGinitie (1970) to measure "flexibility in word meaning."
Items for this test were in part based on research on polysemous words
conducted by Mason, Knisely, and Kendall (1981). In this study the primary
and secondary meanings of words were determined empirically and the effects
of polysemy on reading comprehension were noted. For the present test,
distractors were written to be thematically consistent with the primary
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meaning of the word. Interspersed among 20 items with double meanings were
10 items with only one correct answer. The test was administered in two
separately timed halves of 5 minutes each.
Also measuring semantic knowledge were the Non-Literal and Literal
Vocabulary scales from the Science Research Associates Primary Achievement
battery. These scores were available from both schools' files. The Non-
Literal (VOCABNL) items required comprehension of word meaning in
figurative and idiomatic expressions. In contrast, the Literal (VOCABL)
items required comprehension of words' most literal senses.
Measures of encoding and retrieval. Three instruments were designed
to assess different aspects of encoding and retrieval. The Same or
Different task (ENCRET1) presented the student with two lists of 32 word
pairs. The task was to circle "Same" if the words had the same or similar
meanings, and "Different" if they had clearly different meanings. These
lists were presented with one minute time limits and instructions which
stressed speed and accuracy. Of the 64 word pairs on the lists, only 20
pairs did not contain near-synonyms. In these pairs, the first word was
followed by a high frequency associate with a distinctive meaning. All
words were selected from standardized vocabulary tests designed for third
through fourth graders, thereby lessening the role of vocabulary in
decision time. The resulting score was correct semantic decision rate,
reflecting the speed with which words could be read in, meanings accessed
and represented in working memory (encoded), meanings compared, plus speed
of motor response.
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Two other measures of encoding and retrieval processes were embedded
in an inductive reasoning task. The goal was to construct a measure of the
quality of encoding that transpires when the person is reasoning
inductively such as in a verbal analogy task. If words are being processed
in an appropriate semantic fashion, i.e., attributes are being accessed and
represented in working memory, then memory for these words should be
stronger. A verbal classification test was selected because this task
involves inductive reasoning and it happens to resemble a categorized word
list, adaptable for use in an incidental recall task. Of particular
interest here was the clustering index. Clustering of items of similar
meaning or clustering by category membership would indicate that items have
been organized in memory according to shared semantic features, clear
evidence of semantic analysis of the stimulus words.
This test was labeled "Which Word Does Not fit?" and consisted of four
parts. Part I consisted of eight verbal classification problems in which
the task is to pick the one word which does not belong with the other four
words in the group (time limit: 2 minutes). Part II was a surprise free
recall task. Students were instructed to write down as many words from the
word groups as they could remember (time limit: 3 minutes). Parts III and
IV consisted of 15 verbal classification items each (time limit: 3
minutes).
The free recall task wielded two measures: a total correct recall
score (ENCRET2) and a clustering score (PCCLUS). Parts III and IV of the
test were used as measures of verbal inductive reasoning, one aspect of
discovering semantic relations (DSR1).
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Measures of discovering semantic relations. In addition to DSR1, the
Word Grouping Game (DSR2) and "How Are These Words Related?" (DSR3) were
included as measures of skill at discovering semantic relations.
The Word Grouping Game consisted of two sets of seven words which
could be sorted into groups of varying sizes according to different shared
attributes. The first word set consisted of seven living creatures and the
second set, seven items of food. In separately timed sections (5 minutes
each), students were instructed to write the letter of each word to be
included in the group and then explain what the shared attribute was.
Students began the task by working through detailed instructions with the
experimenter who explained what a valid group would be in several examples.
The "How Are These Words Related" test (DSR3) consisted of two lists
of word pairs representing six of the seven different semantic relations in
analogies identified by Whitely (1977). Whitely's seventh relation, the
word pattern, was not included. The eight relations were the following:
antonyms, synonyms, functional, quantitative, conversion, class-naming,
causation, and property/feature. The last two types were identified in
Millman and Pauk (1969). Thus, the major types of semantic relations in
analogies were represented in the test. Students were instructed to write
a short sentence explaining how the two words were related (time limit: 4
minutes per list). For example, for "cat" and "kitten" a student could
write that a kitten is a baby cat.
Measures of mapping relations. The Written Analogical Reasoning Test
(Gallagher & Wright, 1979) was obtained from the authors as a measure of
the mapping component (MAPR). The WART consists of two parts each with 10
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multiple choice analogy items. Ten items have concrete type relations and
ten have abstract relations. The task is to solve the analogy and then
explain or justify one's choice. For this study the test was renamed the
Solve and Explain test. New instructions were written to enable the
experimenter to demonstrate different forms of explanation that students
could use. Students worked through two examples and discussed each.
Students finished well before the 12 minute limit.
Measures of response evaluation. To measure impulsiveness/
reflectiveness in response evaluation the traditional test was chosen,
i.e., the Matching Familiar Figures test (Kagan et al., 1964). In this
task, students are presented a target picture and six alternatives from
which they are to select the one picture which matches the target
identically. The six alternatives are all very similar to one another,
requiring the student to carefully evalute each one.
This test was administered individually to the students. Latency to
first response (MFFT) and total number of errors (MFFE) were recorded.
Students were instructed to work on each item until they found the right
answer.
Measures of working memory. To measure working memory capacity a
digit span memory test was devised (Case, 1974). The task was presented as
a game "How Many Numbers Can You Remember?" (DSPAN) and was administered to
the entire class, with trial one in the morning, and trial two in the
afternoon.
The experimenter read aloud seven lists of digits, starting with a 3
digit list and ending with a 9 digit list. Before the test the
experimenter practiced reading the lists silently inserting the word
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"thousand" between digits to approximate a one second interval. As the
students listened to the lists, they were instructed to raise their arms
with pencil in hand to prevent any writing. After the last digit, students
attempted to reproduce the number sequences on response sheets.
Results and Discussion
Test Scoring
Most of the 13 tests in the experimental battery could be objectively
scored. Of these tests, only the incidental free recall task and
experimental vocabulary test require further explanation.
The experimental vocabulary test yielded two scores. The regular
vocabulary score (VOCABR) was the number of correct primary meanings
selected from the 20 items with double meanings plus the number of correct
meanings selected from the 10 items with single meanings. The flexibility
score (SEMFLEX) was the number of correct second meanings selected from
items in which a primary meaning was also selected. In other words, a
circled secondary meaning counted toward the flexibility score only if the
primary meaning was also circled.
The incidental free recall task was scored for both number of words
correctly recalled and degree of clustering. The former was scored as the
number of verbatim list words written on the test page, counting misspelled
words but not synonyms. A ratio measure of clustering was chosen after
considering the recommendations of Murphy (1979). The measure chosen was
the simple percentage of words recalled in clusters (i.e., words of same
category grouped together). This measure correlates .95 with the ratio of
repetition but less of its variance is due to confounding variables.
Tests which required judgment on the part of the scorer included the
Solve and Explain test, the "How Are These Words Related?" test and the
Word Grouping Game. Detailed scoring guides were constructed for each of
these tests and 25 test papers were randomly sampled from the 112 papers.
These were scored by another person trained by the experimenter. Inter-
scorer agreement was 93.75% for the "How Are These Words Related?" test and
92.6% for number of valid groups listed on the Word Grouping Game.
Scoring instructions for the Solve and Explain test were modified
somewhat from-the original WART instructions. In the original system an
explanation of an analogy was scored as either symmetric or asymmetric,
with no middle ground. The revised system scales response on a three point
scale. Receiving full credit as symmetric responses are rule reason or
successive reason explanations (Gallagher & Wright, Note 2, 1979).
Receiving half credit are responses which do indicate some understanding of
the analogy but fail to fully demonstrate the symmetry which exists between
domain and range. The relation expressed could apply to both range and
domain, but the student does not bother to demonstrate this, focusing only
on the range. Receiving zero credit are the responses which fail to
compare domain and range, display inversion (A:B::D:C), or appear to state
an associative rule for the answer, e.g., "C and D go together." It should
be noted that asymmetric justifications could be given to correctly solved
analogies. This overall symmetric explanation score correlated .75 with
correct analogy solution.
Inter-scorer agreement was again very high. It was 96% for the
symmetric explanation category, 88.3% for the range--focusing category, and
16
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95.9% for the asymmetric--no comparison category, the most frequent
category. Association proved to be too difficult to distinguish from the
asymmetric--no comparison category.
Reliability estimates for the various tests appear in Table 1. With
the exception of the SRA vocabulary tests, the estimates reported are
split-half correlations corrected with the Spearman-Brown formula. The
Kuder-Richardson Formula 21 was used to estimate the SRA tests'
reliabilities.
Insert Table 1 about here.
Factor Analysis of the Analogy Solution Components
The correlation matrix for the 14 analogy cognitive components was
factored using the principal axes method. Initial estimates of the
communalities were squared multiple correlations. The number of factors to
retain and rotate was decided by the parallel analysis criterion
(Humphreys, Ilgen, McGrath, & Montanelli, 1969). This criterion accepts as
meaningful only those factors with an eigenvalue greater than the
corresponding eigenvalue of a matrix of correlations among random numbers.
These random eigenvalues can be estimated using a regression equation
published in Montanelli and Humphreys (1976). In this case, the random
data eigenvalue for factor five exceeded that of the real data factor five,
so four factors were rotated. Four factor solutions were also indicated by
the Kaiser-Guttman unity criterion and by the maximum likelihood chi-square
test.
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An oblique factor rotation was obtained using the Binormamin program.
The resulting factor intercorrelations suggested a higher order general
factor. Thus, the factor correlations were themselves factored, wielding a
general factor.
It was decided to use the Schmid-Leiman (1957) orthogonalization
procedure which allows one to represent in one matrix the loadings of
observed variables upon higher order factors and upon the primary factors.
Matrix elements are correlations between the variables and that part of the
primary factor which has the higher order factor partialled out. The
pattern matrix Pvo which has v variables as rows and o orthogonal factors
as columns is obtained by the formula: Pvo = Pvf.Af[h + f], in which Pvf
is the primary factor pattern, and Af[h + f] is [PfhlUff], i.e., the higher
order factor patterns augmented by a diagonal matrix whose elements are the
square roots of the uniquenesses of the primary factors.
Table 2 displays the Schmid-Leiman orthogonal factor pattern for the
present data. The factors can be interpreted as follows. The higher order
general factor is probably best regarded as general intelligence. General
intelligence can be defined as that subset of procedural and declarative
knowledge which is most commonly tapped by the various cognitive tasks in
academic settings. The tests which have the highest loadings on this
factor are those which have been traditionally used to measure
intelligence: verbal reasoning (DSR1, DSR3, MAPR) and vocabulary (NLVOC,
LVOC).
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Insert Table 2 about here.
----------------.------- -
The first primary factor was loaded by the error and latency to first
response scores from the Matching Familiar Figure test. This factor is
probably best interpreted as reflectiveness-impulsiveness in evaluating
alternative solutions. In this case, the factor relates well to the
response evaluation component in Sternberg's theory. The role of image
generation, i.e., forming an image of the ideal answer, is probably
minimized in this task since the target picture is readily available. That
these scores load minimally on the general factor is at least in part due
to the visual/figural content of the test. The rest of the battery
involves verbal content.
The second primary factor is a combination of discovering semantic
relationships and semantic flexibility, and thus, corresponds nicely to the
inference component in Sternberg's theory. Discovering how words are
semantically related is important in the word classification task, the word
grouping task, and the identifying semantic relations task. Semantic
flexibility is involved in this factor as well, as indicated by the SEMFLEX
loading. Another type of semantic flexibility is measured by the word
grouping task, which some authors use as a measure of "semantic spontaneous
flexibility" (Hakstian & Cattell, 1974). High scores on this test are
the result of overcoming the cognitive set established by the previously
encoded attributes and searching for new attributes upon which new groups
may be formed.
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The MAPR score loaded on this factor no doubt because of the
involvement of discovering semantic relations, a logical prerequisite of
mapping relations. A student must be able to infer relations between two
concepts before she/he can reflect on higher order relationships between
relations. In the Carroll (1980) re-analysis of Sternberg's data, mapping
and inferring relations also loaded the same factor. In the present study,
however, mapping relations could not be expected to define its own factor
since it was under-represented in the battery.
Percent clustered was included in this battery because of its
sensitivity to encoding semantic attributes. A high degree of clustering
in recall is, in a sense, a record of success in encoding and comparing the
correct semantic attributes of words. It is not surprising that this
measure loads the same factor as tasks requiring the discovery of
relationships.
The two standardized vocabulary tests are the primary variables
loading the third factor. Loading less well is the regular vocabulary
score from the experimental test designed for this study. The standardized
tests required reading comprehension skills at the sentence level, whereas
the new test did not, which may explain its weak loading.
The last factor is best interpreted as the encoding and retrieval
processes factor. The recall task and the semantic decision rate task load
on this factor, but the clustering index does not, contrary to
expectations. Speed of processing can be ruled out as an interpretation
since both the study and recall phases of the incidental recall task had
generous time limits allowing an unspeeded work pace. Instead, what
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appears to be shared by these tasks are the processes of encoding the
meanings of words and retrieving information from memory.
One objection might be that the semantic decision task involves
retrieval from semantic memory and that the recall task involves retrieval
from episodic memory. Kintsch (1977) argues that the distinction between
episodic and semantic memory traces is artificial. The conception of
memory in terms of feature sets applies equally to both kinds of memory.
Retrieval mechanisms are highly similar too. The semantic memory retrieval
model of Smith, Shoben, and Rips (1974) is closely paralleled by the
episodic memory retrieval models of Atkinson and Juola (1974) and Wescourt
and Atkinson (1976). Kintsch's view is supported by the present finding.
Multiple Regression Analyses
Multiple regression modeling is a flexible technique which, through
the hierarchical inclusion method, allows the specification of the causal
priority of variables, either temporally or logically determined (Cohen &
Cohen, 1975). It also allows one to test hypotheses about interactions
between independent variables.
It was decided to work with composite scores representing the analogy
solution components instead of factor scores obtained from the analysis
reported above. It was felt that the factor analysis could have glossed
over subtle differences between independent variables that multiple
regression might be sensitive to. As an example consider that MAPR loaded
the factor with all the DSR tests, but just may explain criterion variance
left unexplained by the DSR composite score.
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For this analysis all variables were transformed to standard scores
and various composites were formed. Semantic knowledge was represented by
a vocabulary composite consisting of VOCABNL, VOCABL, and VOCABR. An
encoding and retrieval processes composite was formed with ENCRET1 and
ENCRET2. Discovering semantic relations was represented by a composite of
DSR1, DSR2, and DSR3. Left as single scores were SEMFLEX, DSPAN, MAPR,
PCCLUS, MFFT and MFFE.
Causal priority was determined by temporal sequence. That is, since
encoding processes would have to operate before an inference could be made,
and inferential processes in turn, would have to operate before any mapping
of relations could occur, these variables were entered in that order into
the equation. After MAPR was entered, MFFT and MFFE were entered, this
order following the logic that response evaluation would occur after the
mapping process.
Two related regression models were tested on both the CART foil errors
(CARTFE) and non-foil errors (CARTNFE). Model A entered VOCAB and DSPAN on
the first step in the hierarchical inclusion process. This allowed one to
determine the influence each predictor had that could not be attributed to
semantic knowledge and working memory capacity. Model B analyses involved
using CARTNFE as the first-entered covariate in the analysis of CARTFE, and
vice versa, to permit another perspective on the data. In all analyses,
the final step was the inclusion of the product terms MFFE X MFFT, PCCLUS X
DSPAN, ENCRET X DSPAN, PCCLUS X DSR, ENCRET X DSR.
As it turns out, CARTNFE and CARTFE overlap substantially (r2 = .46),
reflecting the operation of similar cognitive processes. General
Associative Errors
23
intelligence is operating in both strategies, though perhaps not to the
same degree. This was indicated in the loadings of -.577 for CARTFE and
-.633 for CARTNFE on g, obtained from a Dwyer extension analysis (Dwyer, 1937).
Regression analyses suggest that the two strategy scores are
distinguishable in terms of componential contributions, however. The Model
A analysis in Table 3 shows that for CARTFE significant increments in
explained variance are present for vocabulary (.302), digit span (.097),
percent clustered (.044), semantic flexibility (.045), discovery of
semantic relations (.043), and MFF time (.018). These increments are
squared semi-partial correlations, i.e., correlations between the dependent
variable and independent variable, with the influence of previously entered
independent variables partialed out.
Insert Table 3 about here.
The signs of the regression weights indicate that all relationships
are in the expected directions. Vocabulary and digit span account for the
most variance (30% and 9.7%, respectively) with additional increments of
4.3 to 4.5 percent added by percent clustered, semantic flexibility, and
discovery of semantic relations.
The picture is somewhat different for CARTNFE (see Table 4).
Significant increments in explained variance are due to vocabulary (.431),
digit span (.026), percent clustered (.040), discovery of semantic
relations (.119), and MFF time (.013). In this case, vocabulary and
discovery of semantic relations account for most of the variance (55%).
Associative Errors
24
Insert Table 4 about here.
Before addressing the significance of the differences between the CART
foil and non-foil scores, several findings true of both scores should be
noted. First of all, the CART scores are nearly identical with respect to
the components which reliably predict performance. Contributing to both
scores were semantic knowledge, working memory, encoding and retrieval (as
indexed by percent clustered) discovery of semantic relations and response
evaluation (MFF time). Furthermore, all of the components, with the
exception of mapping relations, contribute to the explained variance. It
is probably the case that the mapping relations score shared too much with
the semantic relations score to explain additional criterion variance. It
should also be noted that an additive model is probably sufficient for
these data since all product terms failed to add significantly to the
explained variance. Included here is the MFF error by latency term,
indicating that impulsiveness is not likely to play an important role.
Perhaps though, something akin to time spent encoding stimuli and
evaluating alternatives is important, given the significant MFF time semi-
partial correlation.
To test the differences between the contributions made by each
component to the criteria, the t-test for the difference between two
correlations for a single sample was applied to the semi-partial
correlations (Ferguson, 1971). These t-tests show that vocabulary probably
plays a more important role in non-associative errors (semi-partial r =
Associative Errors
25
-.656) than in associative errors (semi-partial r = -.549), t(109) = 1.8, p
< .065. This is also true of the DSR component (semi-partial r equals
-.345, -.207, respectively), t(104) = 1.86, p < .065. On the other hand,
working memory capacity plays a larger role in associative errors (semi-
partial r = -.311), than in non-associative errors (semi-partial, r =
-.162), t(108) = -2.04, p < .05.
Another way to examine differences between the cognitive components of
associative and non-associative errors is to use one error score as a
covariate in the prediction of the other. Variables entered into the
equation after the covariate will show increments in explained variance not
attributable to the covariate.
Tables 5 and 6 display the Model B analyses for the associative and
non-associative error scores respectively. With non-associative variance
controlled, associative variance is explained in increments by vocabulary
(.019), digit span (.051), and semantic flexibility (.021). With
associative variance controlled, significant increments in non-associative
variance are found for vocabulary (.115), and discovery of semantic
relations (.078). These analyses corroborate the earlier findings and
suggest also that semantic flexibility plays a larger role in the events
leading to the associative type error.
---------------------------Insert Tables 5 and 6 about here.
Insert Tables 5 and 6 about here.
Associative Errors
26
General Discussion
This study lends partial support to Sternberg's theory of analogical
reasoning by demonstrating that encoding and retrieval processes, semantic
inference processes, and something akin to response evaluation each predict
analogy performance when entered into a regression equation in a theory-
specified order. This study also demonstrates the importance of
vocabulary, working memory capacity, and semantic flexibility in the
solution of verbal analogies.
Most importantly, it was found that the associative and non-
associative error types overlap considerably in underlying cognitive
processes. Every component, with the exception of MAPR, explained variance
in CARTFE and CARTNFE. The strengths of these contributions differed in
interesting ways, however. Semantic knowledge and discovery of semantic
relations appear to have stronger roles in the events leading to the non-
associative error than in those leading to the associative error. On the
other hand, working memory capacity and semantic flexibility appear to have
greater importance in the events leading to the associative response.
These findings can be tentatively interpreted to mean that when
association is not available or is avoided in analogy solution, great
reliance is placed upon semantic knowledge and the ability to reason
inductively with words. Together these components account for 55 percent
of the variance. When association is employed in analogy solution, this
could be the result of limited working memory capacity and perhaps,
inflexibility in accessing the meanings of analogy terms, or some other
related kind of inflexibility. Working memory and semantic flexibility
---------------------------------
Associative Errors
27
account for only 9.7% and 4.5% of the variance, respectively, so much
of the unique nature of the associative strategy remains to be explained.
There are several areas that need further exploration in the search
for the cognitive events leading to the associative response. One
interesting finding was that working memory capacity was more strongly
related to associative errors. Research has shown that associative errors
decrease in frequency as the child develops (Achenbach, 1971; Sternberg &
Nigro, 1980), and that working memory capacity increases (Case, 1974). A
potential link between working memory and associative errors could be the
inference component. Previous research has shown that limited working
memory adversely affects the inference process (Kotovsky & Simon, 1973;
Holzman, Pellegrino, & Glaser, 1982). With only a vague idea of how A and
B are related because of an inability to effectively compare attribute
lists in working memory, the student may have a lower criterion of
acceptability for a relationship in the range. As a consequence, the
salient, associative relationship is chosen.
A second area needing further exploration is the relationship between
mapping relations and associative responding. In this study mapping
relations did not add significantly to the prediction of either CARTFE or
CARTNFE, when entered in its theory-specified position. Simple
correlations were quite strong (-.562 for CARTFE, -.529 for CARTNFE), but
because a highly correlated variable (DSR) was entered first, MAPR could
not add to the explained variance.
Final assessment of the mapping relations component must be postponed
until additional measures of this type of reasoning can be developed.
Associative Errors
28
Under-representation in the test battery probably diminished its chances of
demonstrating its unique nature and role in explaining associative score
variance. One possible direction for new measures is suggested by the
similarity of proportional and analogical reasoning (for review see
Gallagher & Mansfield, 1980). A proportion is a kind of quantitative
analogy. Recognition that 1 is to 2 as 3 is to 6 implies 1 is to 3 as 2 is
to 6 indicates a higher order understanding of proportionality that
parallels the understanding of analogy reflected in symmetric rule reasons
given as analogy answer justifications.
In conclusion, this study has pointed to several differences between
associative and non-associative errors in analogical reasoning. The next
step for research should be to design an experiment in which vocabulary
difficulty, ease of inference, demands upon working memory capacity, and
perhaps polysemy of analogy terms are varied factorially. Such
experimentation should allow a more definitive assessment of the
importance of these components in associative and non-associative errors.